A222209 Inverse of permutation in A222208.

1, 3, 2, 5, 7, 4, 11, 9, 13, 17, 19, 6, 23, 29, 14, 15, 31, 8, 37, 21, 22, 41, 43, 10, 47, 53, 26, 25, 59, 28, 61, 27, 38, 67, 49, 12, 71, 73, 46, 35, 79, 33, 83, 57, 89, 97, 101, 18, 103, 51, 62, 69, 107, 16, 109, 55, 74, 113, 127, 34, 131, 137, 121, 45, 139

Offset: 1

Author

Alois P. Heinz, Feb 12 2013

Keywords

• nonn
• look

Comments

Permutation of the natural numbers A000027 with inverse permutation A222208.

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A000027, A211384, A222208.

Programs

Haskell

import Data.List (elemIndex)
import Data.Maybe (fromJust)
a222209 = (+ 1) . fromJust . (`elemIndex` a222208_list)
-- Reinhard Zumkeller, Feb 13 2013

Maple

b:= proc(n) false end:
g:= proc(n) option remember; local h, i;
      if n<3 then h:= 2*n-1 else g(n-1); h:= ilcm(map(g,
         numtheory[divisors](n) minus {1, n})[]) fi;
      for i while b(i*h) do od;
      b(i*h):= true; i*h
    end:
a:= proc() local t, a; t, a:= -1, proc() -1 end;
      proc(n) local h;
        while a(n) = -1 do
          t:= t+1; h:= g(t);
          if a(h) = -1 then a(h):= t fi
        od; a(n)
      end
    end():
seq(a(n), n=1..100);

Mathematica

terms = 100; b[1] = 1; b[2] = 3; b[n_] := b[n] = Module[{d, s, c, k}, d = Divisors[n] ~Complement~ {1, n}; For[s = Sort[Array[b, n - 1]]; c = Complement[ Range[ Last[s]], s]; k = If[c == {}, Last[s] + 1, First[c]], True, k++, If[FreeQ[s, k], If[AllTrue[d, Divisible[k, b[#]] &], Return[k]]]]]; a[n_] := a[n] = For[k = 1, True, k++, If[b[k] == n, Return[k]]]; Array[a, terms] (* Jean-François Alcover, Feb 22 2018 *)